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A. Fathi (1997)
Partitions of Unity for Countable CoversAmerican Mathematical Monthly, 104
F. Wilson, J. Yorke (1973)
Lyapunov functions and isolating blocksJournal of Differential Equations, 13
T. Nadzieja (1990)
Construction of a smooth Lyapunov function for an asymptotically stable setCzechoslovak Mathematical Journal, 40
C. Conley, R. Easton (1971)
Isolated invariant sets and isolating blocksTransactions of the American Mathematical Society, 158
P. Bernard, S. Suhr (2017)
Smoothing causal functionsJournal of Physics: Conference Series, 968
A Fathi (2011)
87Pub. Matemáticas del Uruguay, 12
F. Laudenbach, J. Sikorav (1994)
Hamiltonian disjunction and limits of Lagrangian submanifoldsInternational Mathematics Research Notices, 1994
J. Duistermaat, L. Hörmander (1972)
Fourier integral operators. IIActa Mathematica, 128
A. Fathi, A. Siconolfi (2011)
On smooth time functionsMathematical Proceedings of the Cambridge Philosophical Society, 152
Y. Egorov, M. Shubin (1994)
Fourier Integral Operators
A. Fathi, P. Pageault (2017)
Smoothing Lyapunov functionsTransactions of the American Mathematical Society
A. Siconolfi, Gabriele Terrone (2007)
A metric approach to the converse Lyapunov theorem for continuous multivalued dynamicsNonlinearity, 20
(2011)
On existence of smooth critical subsolutions of the Hamilton – Jacobi equation
(1961)
Converse theorems of Lyapunov's second method
(1956)
On the inversion of Lyapunov ’ s second theorem on stability of motion
G. Paternain, L. Polterovich, K. Siburg (2002)
Boundary rigidity for Lagrangian submanifolds, non-removable intersections, and Aubry-Mather theoryMoscow Mathematical Journal, 3
A Fathi (1997)
720Am. Math. Mon., 104
GP Paternain, L Polterovich, KF Siburg (2003)
Boundary rigidity for Lagrangian submanifolds, non-removable intersections, and Aubry–Mather theoryMosc. Math. J., 3
D. Sullivan (1976)
Cycles for the dynamical study of foliated manifolds and complex manifoldsInventiones Mathematicae, 36
P. Bernard, S. Suhr (2015)
Lyapounov Functions of Closed Cone Fields: From Conley Theory to Time FunctionsCommunications in Mathematical Physics, 359
J. Massera (1956)
Contributions to Stability TheoryAnnals of Mathematics, 64
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JR. WILSON (1969)
Smoothing derivatives of functions and applicationsTransactions of the American Mathematical Society, 139
We give a simpler proof of the existence of isolating blocks due to Conley and Easton (Trans Am Math Soc 158:35–61, 1983) based on a generalization of the work of Wilson Jr. and Yorke (J Differ Equ 13:106–123, 1973) on Lyapunov functions and isolating blocks. This will also yield a proof of Massera’s (Ann Math 64:182–206, 1956) converse Lyapunov Theorem and a proof of a Theorem independently due to Duistermaat and Hörmander (Acta Math 128:183–269, 1972) and Sullivan (Invent Math 36:225–255, 1976).
"Bulletin of the Brazilian Mathematical Society, New Series" – Springer Journals
Published: Sep 1, 2022
Keywords: Flow; Smooth Lyapunov; Converse Lyapunov; Isolating block
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